A212513 - OEIS

%I #8 Dec 18 2015 07:53:18

%S 0,1,16,72,210,483,990,1760,2964,4680,7040,10176,14364,19551,26180,

%T 34320,44200,56025,70308,86800,106330,128898,154836,184416,218448,

%U 256373,299520,347760,401534,461175,527850,600576,681296,769692,866320,971568,1087020

%N Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y<=3z.

%C For a guide to related sequences, see A211795.

%H Colin Barker, <a href="/A212513/b212513.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,0,2,0,-2,0,4,1,-2,-2,0,1).

%F a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).

%F G.f.: x*(1 +16*x +70*x^2 +176*x^3 +308*x^4 +446*x^5 +510*x^6 +514*x^7 +471*x^8 +372*x^9 +220*x^10 +102*x^11 +30*x^12 +4*x^13) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - _Colin Barker_, Dec 18 2015

%t t = Compile[{{n, _Integer}}, Module[{s = 0},

%t (Do[If[w <= 2 x && y <= 3 z, s = s + 1],

%t {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

%t Map[t[#] &, Range[0, 50]]   (* A212513 *)

%o (PARI) concat(0, Vec(x*(1 +16*x +70*x^2 +176*x^3 +308*x^4 +446*x^5 +510*x^6 +514*x^7 +471*x^8 +372*x^9 +220*x^10 +102*x^11 +30*x^12 +4*x^13) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ _Colin Barker_, Dec 18 2015

%Y Cf. A211795, A212508.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, May 20 2012